๐ Understanding One-Step Subtraction Equations
One-step subtraction equations involve isolating a variable by performing the opposite operation of subtraction, which is addition. The goal is to get the variable alone on one side of the equation.
- ๐ Definition: An equation where a number is subtracted from a variable, represented as $x - a = b$.
- โ Solving: Add the number being subtracted ($a$) to both sides of the equation to isolate $x$: $x - a + a = b + a$, which simplifies to $x = b + a$.
- ๐ข Example: Solve $x - 5 = 12$. Add 5 to both sides: $x - 5 + 5 = 12 + 5$, so $x = 17$.
โ Understanding One-Step Addition Equations
One-step addition equations involve isolating a variable by performing the opposite operation of addition, which is subtraction. Again, the aim is to get the variable by itself.
- ๐ Definition: An equation where a number is added to a variable, represented as $x + a = b$.
- โ Solving: Subtract the number being added ($a$) from both sides of the equation to isolate $x$: $x + a - a = b - a$, which simplifies to $x = b - a$.
- ๐ข Example: Solve $x + 3 = 9$. Subtract 3 from both sides: $x + 3 - 3 = 9 - 3$, so $x = 6$.
๐ Comparison Table: Subtraction vs. Addition Equations
| Feature |
One-Step Subtraction Equations |
One-Step Addition Equations |
| General Form |
$x - a = b$ |
$x + a = b$ |
| Operation to Isolate Variable |
Addition (add $a$ to both sides) |
Subtraction (subtract $a$ from both sides) |
| Solution |
$x = b + a$ |
$x = b - a$ |
| Example |
$x - 7 = 10 \Rightarrow x = 10 + 7 = 17$ |
$x + 4 = 15 \Rightarrow x = 15 - 4 = 11$ |
๐ก Key Takeaways
- ๐ Inverse Operations: Remember, solving these equations relies on using inverse operations. Addition is the inverse of subtraction, and vice versa.
- โ๏ธ Balance: Always perform the same operation on both sides of the equation to maintain balance.
- โ๏ธ Checking Your Work: Substitute your solution back into the original equation to verify that it's correct.